function [p,plo,pup] = normcdf(x,mu,sigma,pcov,alpha)
%NORMCDF Normal cumulative distribution function (cdf).
%   P = NORMCDF(X,MU,SIGMA) returns the cdf of the normal distribution with
%   mean MU and standard deviation SIGMA, evaluated at the values in X.
%   The size of P is the common size of X, MU and SIGMA.  A scalar input
%   functions as a constant matrix of the same size as the other inputs.
%
%   Default values for MU and SIGMA are 0 and 1, respectively.
%
%   [P,PLO,PUP] = NORMCDF(X,MU,SIGMA,PCOV,ALPHA) produces confidence bounds
%   for P when the input parameters MU and SIGMA are estimates.  PCOV is a
%   2-by-2 matrix containing the covariance matrix of the estimated parameters.
%   ALPHA has a default value of 0.05, and specifies 100*(1-ALPHA)% confidence
%   bounds.  PLO and PUP are arrays of the same size as P containing the lower
%   and upper confidence bounds.
%
%   See also ERF, ERFC, NORMFIT, NORMINV, NORMLIKE, NORMPDF, NORMRND, NORMSTAT.

%   References:
%      [1] Abramowitz, M. and Stegun, I.A. (1964) Handbook of Mathematical
%          Functions, Dover, New York, 1046pp., sections 7.1, 26.2.
%      [2] Evans, M., Hastings, N., and Peacock, B. (1993) Statistical
%          Distributions, 2nd ed., Wiley, 170pp.

%   Copyright 1993-2011 The MathWorks, Inc.
%   $Revision: 1.1.6.4 $  $Date: 2011/05/09 01:26:18 $

% if nargin<1
%     error(message('stats:normcdf:TooFewInputsX'));
% end
% if nargin < 2
%     mu = 0;
% end
% if nargin < 3
%     sigma = 1;
% end

% More checking if we need to compute confidence bounds.
% if nargout>1
%    if nargin<4
%       error(message('stats:normcdf:TooFewInputsCovariance'));
%    end
%    if ~isequal(size(pcov),[2 2])
%       error(message('stats:normcdf:BadCovarianceSize'));
%    end
%    if nargin<5
%       alpha = 0.05;
%    elseif ~isnumeric(alpha) || numel(alpha)~=1 || alpha<=0 || alpha>=1
%       error(message('stats:normcdf:BadAlpha'));
%    end
% end

% try
    z = (x-mu) ./ sigma;
% catch
%     error(message('stats:normcdf:InputSizeMismatch'));
% end

% Prepare output
p = NaN(size(z),class(z));
% if nargout>=2
%     plo = NaN(size(z),class(z));
%     pup = NaN(size(z),class(z));
% end

% Set edge case sigma=0
p(sigma==0 & x<mu) = 0;
p(sigma==0 & x>=mu) = 1;
% if nargout>=2
%     plo(sigma==0 & x<mu) = 0;
%     plo(sigma==0 & x>=mu) = 1;
%     pup(sigma==0 & x<mu) = 0;
%     pup(sigma==0 & x>=mu) = 1;
% end

% Normal cases
% if isscalar(sigma)
%     if sigma>0
        todo = true(size(z));
%     else
%         return;
%     end
% else
%     todo = sigma>0;
% end
z = z(todo);

% Use the complementary error function, rather than .5*(1+erf(z/sqrt(2))),
% to produce accurate near-zero results for large negative x.
p(todo) = 0.5 * erfc(-z ./ sqrt(2));

% Compute confidence bounds if requested.
% if nargout>=2
%    zvar = (pcov(1,1) + 2*pcov(1,2)*z + pcov(2,2)*z.^2) ./ (sigma.^2);
%    if any(zvar<0)
%       error(message('stats:normcdf:BadCovarianceSymPos'));
%    end
%    normz = -norminv(alpha/2);
%    halfwidth = normz * sqrt(zvar);
%    zlo = z - halfwidth;
%    zup = z + halfwidth;
% 
%    plo(todo) = 0.5 * erfc(-zlo./sqrt(2));
%    pup(todo) = 0.5 * erfc(-zup./sqrt(2));
% end
